Meeting the man behind Spitting Image's rubbery Maggie.

It’s one of the stranger sentences ever uttered about Margaret Thatcher. “I must have been 15 – it was 1975 when she became leader – and I just sat down one day, and out she came, fully formed.” You could be forgiven for thinking Steve Nallon is talking about some kind of supernatural experience, and in a way he is – except that what “came out” wasn’t a ghost or an apparition, but an impression so good that it’s been central to his life ever since.

“I started doing it at school and then I did it in the northern comedy clubs. At university and then at the Fringe, someone lent me a frock and I started doing it in full costume,” he says. All this experience came in handy when, in 1984, Nallon joined the cast of a new satirical programme on ITV called Spitting Image. The combination of his Thatcher impression and the now-iconic puppet was a great success, and he went on to work on the show for the next 12 years.

Now, 30 years after the first episode, he is looking back. “People think because I do Thatcher that I’m obsessed by her, that I’ve got every book ever written on her, which I don’t … I’m not especially interested in her,” he chuckles. “I had to be, in the Eighties, because of my act. It was a joy when she went because I didn’t have to read the endless newspaper articles any more.”

The voice is as good as ever, though. It’s uncanny, watching Nallon become Thatcher. He drops into it with great ease mid-sentence. His mouth tightens into the slight pout the Iron Lady always had and his posture changes – leaning forward, he tells me with all the solemnity of a prime minister greeting a fellow head of state that he thinks the Two Ronnies are very funny and then wonders: “Could one Ronnie do the joke just as well?”

Naturally, it wasn’t just Thatcher – Nallon voiced all kinds of other characters on Spitting Image. When he does his Alan Bennett for me, he explains that it’s all down to the top lip. “It’s very tense, it’s not going to let you in to any secrets,” he says in Bennett’s voice. In fact, Nallon and Bennett have more in common than just intonation. Both come from working-class backgrounds in Leeds and after moving south to work in the arts “didn’t quite fit in in either place”.

Nallon feels his working-class roots helped him capture Thatcher in a way few other impressionists have been able to do. “I’ve got the background most Labour MPs would die for – cobbled streets, outside loos, tin baths … But it wasn’t a Labour, union sort of family. It was Thatcherite, Tory.”

Understanding this helped him replicate the self-belief Thatcher projected so strongly. Other impressionists, he says, make her too “knowingly patronising” and don’t appreciate that a good impression isn’t just a matter of impersonating someone. “It’s got to be slightly more real than they are,” he explains. There’s an element of caricature, too. The Spitting Image puppets helped with this, but some of it has to be in the voice. “By the end, my Thatcher didn’t sound anything like her,” Nallon says. “It was an alternative-reality version, a parallel universe.”

This month, Nallon took to the stage as Thatcher for the first time since she died last April. He’s had to rewrite his act completely, as the former PM now speaks from the afterlife. “Of course, being dead has its liberations,” he declaims in her voice, then flips back into his own. “I’m only going to do it for ten minutes – God knows I don’t want to make a career out of it.”

“Spitting Image at 30” will take place on Thursday 27 February at BFI Southbank, London SE1, and will include a preview of “Arena: Whatever Happened to Spitting Image”, a new film for BBC4 directed by Anthony Wall